A185996 Coefficient array of orthogonal polynomials P(n,x)=(x-2n+2)*P(n-1,x)-(2n-3)*P(n-2,x), P(0,x)=1, P(1,x)=x-1.

1, -1, 1, 1, -3, 1, -1, 10, -7, 1, 1, -46, 47, -13, 1, -1, 299, -373, 144, -21, 1, 1, -2577, 3606, -1696, 345, -31, 1, -1, 27636, -41746, 22374, -5605, 706, -43, 1, 1, -353404, 565202, -332934, 96359, -15086, 1295, -57, 1, -1, 5239925, -8770446, 5556536, -1790603, 327145, -35161, 2192, -73, 1, 1, -88310783, 153499519, -103128216, 36149287, -7422751, 938028, -73648, 3489, -91, 1

Offset

0,5

Links

Table of n, a(n) for n=0..65.

E. Deutsch, L. Ferrari and S. Rinaldi, Production Matrices, Advances in Applied Mathematics, 34 (2005) pp. 101-122.

Example

Triangle begins
   1,
  -1, 1,
   1, -3, 1,
  -1, 10, -7, 1,
   1, -46, 47, -13, 1,
  -1, 299, -373, 144, -21, 1,
   1, -2577, 3606, -1696, 345, -31, 1,
  -1, 27636, -41746, 22374, -5605, 706, -43, 1,
   1, -353404, 565202, -332934, 96359, -15086, 1295, -57, 1,
  -1, 5239925, -8770446, 5556536, -1790603, 327145, -35161, 2192, -73, 1
Production matrix of inverse begins
  1, 1,
  1, 2, 1,
  0, 3, 4, 1,
  0, 0, 5, 6, 1,
  0, 0, 0, 7, 8, 1,
  0, 0, 0, 0, 9, 10, 1,
  0, 0, 0, 0, 0, 11, 12, 1,
  0, 0, 0, 0, 0, 0, 13, 14, 1,
  0, 0, 0, 0, 0, 0, 0, 15, 16, 1

Crossrefs

Cf. A178120.

Inverse is A185997.

Sequence in context: A263864 A060543 A267751 * A261215 A176157 A176156

Adjacent sequences: A185993 A185994 A185995 * A185997 A185998 A185999

Keyword

sign,easy,tabl

Author

Paul Barry, Feb 08 2011

Status

approved